A333982 a(0) = 0; a(n) = 3^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 3^(k-1) * (n-k) * a(n-k).

0, 1, 5, 48, 909, 28836, 1371384, 91308708, 8106024861, 925225277004, 132007041682380, 23019553116101268, 4817014157800460664, 1191268407723761654964, 343706793228408937835772, 114423311913128119741898268, 43534429651349601213257298621, 18771927426013054800534345817884, 9106204442628918977341144456510260

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((4 - BesselI(0,2*sqrt(3*x))) / 3).

Mathematica

a[0] = 0; a[n_] := a[n] = 3^(n - 1) + (1/n) Sum[Binomial[n, k]^2 3^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[-Log[(4 - BesselI[0, 2 Sqrt[3 x]])/3], {x, 0, nmax}], x] Range[0, nmax]!^2

Crossrefs

Cf. A102223, A201355, A333981, A333983, A333984, A333985, A337593.

Sequence in context: A352254 A346183 A224510 * A063429 A297856 A298091

Adjacent sequences: A333979 A333980 A333981 * A333983 A333984 A333985

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 04 2020

Status

approved